Spin-flavor entanglement in $\Lambda_b \to \Lambda D$ and weak phase extraction

TL;DR

This paper uncovers a novel spin-flavor entanglement in $ ext{Lambda}_b$ decays, linking it to decay rates and Lee-Yang parameters, and proposes a new method for measuring the weak phase $oldsymbol{ extgamma}$ with precision tied to entanglement.

Contribution

It introduces a new spin-flavor entanglement structure in $ ext{Lambda}_b$ decays and leverages it for a novel weak phase measurement method.

Findings

Entanglement encodes in decay rates and Lee-Yang parameters.

The weak phase uncertainty scales inversely with the Wootters concurrence.

Provides a quantitative link between entanglement and measurement precision.

Abstract

We identify a new spin-flavor entanglement structure in $\Lambda_b\to\Lambda D$ decays, formed by the correlation between the $\Lambda$ spin and the $D$ flavor states ($D=D^0,\overline D^0,D_1,D_2$). The entanglement information is encoded in the decay rates and Lee-Yang parameters of the four neutral-$D$ modes. We then show that the same spin-flavor structure provides a new method to determine the weak phase $\gamma$, a key angle of the Cabibbo-Kobayashi-Maskawa unitarity triangle. We find that the experimental uncertainty scales as $\sigma_\gamma\propto 1/{\cal C}$, where ${\cal C}$ is the Wootters concurrence, thereby quantitatively relating the precision of the weak-phase extraction to the amount of spin-flavor entanglement.